SOLUTION: *True OR false* IF f’(x) =g’(x) then f(x) - g(x) = zero

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Question 1158582: *True OR false*
IF f’(x) =g’(x) then
f(x) - g(x) = zero

Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


False.

f(x) and g(x) can differ by a constant.

Example:
f(x) = 2x; g(x) = 2x+5
f'(x) = 2; g'(x) = 2

If you think of the derivative as giving the slope of the graph of a linear equation, the statement shown would say that if two lines have the same slope then they are the same line. Obviously that is not true.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

IF f’%28x%29 =g’%28x%29 then
f%28x%29+-+g%28x%29+=+zero=> false
explanation:
->according to mean value theorem: If f’%28x%29 =g’%28x%29for all x in an interval (a,b) then in this interval we have
f%28x%29=g%28x%29%2Bc where c is some+constant.


so, f’%28x%29 =g’%28x%29 then f%28x%29+-+g%28x%29+= some constant C would be true